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Question: Answered & Verified by Expert
Two gases A and B are at absolute temperatures $360 \mathrm{~K}$ and $420 \mathrm{~K}$ respectively. The ratio of average kinetic energy of the molecules of gas B to that of gas A is
PhysicsKinetic Theory of GasesMHT CETMHT CET 2022 (05 Aug Shift 2)
Options:
  • A $6: 7$
  • B $\sqrt{7}: \sqrt{6}$
  • C $7: 6$
  • D $49: 36$
Solution:
2444 Upvotes Verified Answer
The correct answer is: $7: 6$
The mean kinetic energy $\frac{1}{2} \mathrm{~m}<\mathrm{v}>^2$ of the gas molecule is proportional to the temperature $\mathrm{T}$.
$\frac{\mathrm{K}_{\mathrm{B}}}{\mathrm{K}_{\mathrm{A}}}=\frac{\mathrm{T}_{\mathrm{B}}}{\mathrm{T}_{\mathrm{A}}}=\frac{420}{360}=\frac{7}{6}$

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